REVIEW
Scalar Dark Matter candidates
High Energy Physics - Phenomenology · Submitted 23 May 2003 · 50 references
Pith's verdict: An early, honest, and still-useful paper that made sub-GeV scalar dark matter a legitimate thing to compute — the U-boson branch is the part that lasted, and the F branch is soft in a way the authors themselves flag.
T0 · AI review
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Referee report
The paper
The paper claims
Scalar dark matter may exist between a few MeV and a few GeV, because scalars are not bound by the Lee-Weinberg argument that rules out light fermionic dark matter.
The reading
What carries the argument
The load-bearing object is the annihilation cross section of a scalar pair into a fermion-antifermion pair, computed in the local limit $m_F, m_U gg m_{dm} ge m_f$. For $F$ exchange with non-chiral couplings, $sigma_{ann} v_{rel} simeq frac{1}{4pi} sqrt{1 - m_f^2/m_{dm}^2} (1 - m_f^2/m_{dm}^2 + v_{dm}^2) C_l^2 C_r^2/m_F^2$ for non-self-conjugate dark matter, four times larger for the self-conjugate case. The mass of the dark matter particle appears only inside the phase-space factor, which is what breaks the link between $m_{dm}$ and $Omega_{dm} h^2$. For $U$ exchange the amplitude is proportional to the momentum transfer carried by the derivative coupling, giving $sigma_{ann} v_{rel} propto v_{dm}^2 C_U^2 [4 m_{dm}^2 (f_{Ul}^2 + f_{Ur}^2) - m_f^2(f_{Ul}^2 - 6 f_{Ul} f_{Ur} + f_{Ur}^2)]/(m_U^2 - 4 m_{dm}^2)^2$. That built-in velocity suppression is what lets the same particle satisfy the relic density at freeze-out and produce a negligible photon flux today. The paper also derives the elastic dark matter-neutrino cross section, which for non-self-conjugate scalars goes as $C_l^4 T^2/(48 pi m_F^4)$ and vanishes identically for self-conjugate scalars because the $t$- and $u$-channel amplitudes cancel in the local limit.
Extended reading notes
Core claim
The central claim is that scalar dark matter with a mass between roughly a few MeV and a few GeV can simultaneously reproduce the observed relic density and stay below the gamma-ray limits, contrary to the usual assumption that anything below a few GeV overcloses the universe. Two mechanisms carry this. In the first, the scalar couples to a heavy fermion $F$ (a mirror partner of an ordinary fermion) through non-chiral Yukawa couplings $C_l$ and $C_r$; the annihilation cross section then goes as $C_l^2 C_r^2/m_F^2$ with essentially no dependence on $m_{dm}$, so the relic density constrains $C_l C_r/m_F$ rather than the dark matter mass. In the second, the scalar couples to a new light gauge boson $U$ through a derivative coupling, so the annihilation cross section is proportional to $v_{dm}^2$ and the constant, S-wave piece vanishes identically. The two routes differ sharply under the gamma-ray constraint: for $m_{dm} < 100$ MeV the $F$-exchange route produces too many photons unless the particle and antiparticle number densities are asymmetric, while the $U$-boson route is naturally suppressed by two powers of the present-day dark matter velocity and survives. The authors also compute collisional damping from elastic scattering on neutrinos and find it small, at most tens of solar masses in the most favourable case, so the linear and non-linear power spectra should look like cold dark matter.
Load-bearing premise
For the heavy-fermion branch, the relic density needs $C_l C_r$ of order $10^{-2}(m_F/100,mathrm{GeV})$ while the muon anomalous magnetic moment allows only about $10^{-3}(m_F/100,mathrm{GeV})$, and the paper resolves this by asserting that an additional charged scalar and neutral fermion with masses tuned so that $m_{F^-} approx 11.8, m_H$ will cancel the excess; no such model is built and the stability of that tuning is not examined.
Editorial extensions
If this is right
- A scalar in the MeV-to-GeV window coupled to a light $U$ boson would leave a low-energy gamma-ray signature from the galactic centre, with a predicted flux around $2 times 10^{-5} (m_{dm}/mathrm{MeV})^{-2} mathrm{cm}^{-2} mathrm{s}^{-1}$ for a Navarro-Frenk-White profile, close to existing limits for $m_{dm}$ near 1 MeV.
- For the $F$-exchange branch below 100 MeV, the particle-antiparticle asymmetry is not optional: without it the residual annihilations exceed the observed gamma-ray flux, so any such model must explain where the asymmetry came from.
- The heavy mirror fermions and the extra scalars needed to cancel their contribution to the muon and electron anomalous magnetic moments should sit within reach of the LHC, making the $F$ branch testable by direct search rather than only by cosmology.
- Because the damping scale stays below the smallest observed primordial structures, the matter power spectrum and the cosmic microwave background should be indistinguishable from cold dark matter, so structure formation cannot be used to confirm or exclude these candidates.
- An $N=2$ extended supersymmetry or extra-dimensional framework supplies a naturally stable spin-0 partner of a gauge boson, protected by a mirror parity analogous to $R$-parity, which makes the light scalar a generic prediction of those constructions rather than an added ingredient.
Reading between the lines
- The two branches are not equally exposed to experiment: the $U$-boson branch predicts a specific low-energy photon flux that scales as $m_{dm}^{-2}$, so a modest improvement in MeV-band gamma-ray sensitivity would probe the low-mass end of the window directly.
- The paper's own numbers suggest the $F$ branch lives or dies on a fine-tuned spectrum, so a natural follow-up is to ask whether the required near-degeneracy among the charged scalar, the neutral fermion, and the mirror fermion can survive radiative corrections at all.
- If the $U$ boson decays predominantly into dark matter pairs, as the lifetime estimate of about $10^{-15}$ s with a branching ratio near $6 times 10^{-2}$ into fermions suggests, then the standard single-photon plus missing-energy searches at colliders would have missed it, which is a concrete and checkable loophole.
- The velocity-suppressed annihilation means residual annihilation was more important at higher redshift; a careful treatment of annihilation inside forming structures could turn this from a nuisance into a signature, for instance as a source of early reionization photons.
Original abstract
We investigate the possibility that Dark Matter (dm) could be made of scalar candidates and focus, in particular, on the unusual mass range between a few MeV's and a few GeV's. After showing why the Lee-Weinberg limit (which usually forbids a dm mass below a few GeV's) does not necessarily apply in the case of scalar particles, we discuss how light candidates (mdm < O(GeV)) can satisfy both the gamma ray and relic density constraints. We find two possibilities. Either dm is coupled to heavy fermions (but if $mdm \lesssim 100$ MeV, an asymmetry between the dm particle and antiparticle number densities is likely to be required), or dm is coupled to a new light gauge boson U. The (collisional) damping of light candidates is, in some circumstances, large enough to be mentioned, but in most cases too small to generate a non linear matter power spectrum at the present epoch that differs significantly from the Cold Dark Matter spectrum. On the other hand, heavier scalar dm particles (ie with $mdm \gtrsim O(GeV)$) turn out to be much less constrained. We finally discuss a theoretical framework for scalar candidates, inspired from theories with N=2 extended supersymmetry and/or extra space dimensions, in which the dm stability results from a new discrete (or continuous) symmetry.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We investigate the possibility that Dark Matter (dm) could be made of scalar candidates and focus, in particular, on the unusual mass range between a few MeV's and a few GeV's. After showing why the Lee-Weinberg limit (which usually forbids a dm mass below a few GeV's) does not necessarily apply in the case of scalar particles, we discuss how light candidates (mdm < O(GeV)) can satisfy both the gamma ray and relic density constraints. We find two possibilities. Either dm is coupled to heavy fermions (but if $mdm \lesssim 100$ MeV, an asymmetry between the dm particle and antiparticle number densities is likely to be required), or dm is coupled to a new light gauge boson U. The (collisional) damping of light candidates is, in some circumstances, large enough to be mentioned, but in most cases too small to generate a non linear matter power spectrum at the present epoch that differs significantly from the Cold Dark Matter spectrum. On the other hand, heavier scalar dm particles (ie with $mdm \gtrsim O(GeV)$) turn out to be much less constrained. We finally discuss a theoretical framework for scalar candidates, inspired from theories with N=2 extended supersymmetry and/or extra space dimensions, in which the dm stability results from a new discrete (or continuous) symmetry.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the possibility that Dark Matter (dm) could be made of scalar candidates and focus, in particular, on the unusual mass range between a few MeV's and a few GeV's. | contribution 0.97 | 0.80 | 0.05 | hedged possibility 0.99 |
| s1 | After showing why the Lee-Weinberg limit (which usually forbids a dm mass below a few GeV's) does not necessarily apply in the case of scalar particles, we discuss how light candidates (mdm < O(GeV)) can satisfy both the gamma ray and relic density constraints. | contribution 0.68 | 0.72 | 0.21 | asserted 0.78 |
| s2 | We find two possibilities. | result 0.94 | 0.88 | 0.05 | asserted 0.94 |
| s3 | Either dm is coupled to heavy fermions (but if $mdm \lesssim 100$ MeV, an asymmetry between the dm particle and antiparticle number densities is likely to be required), or dm is coupled to a new light gauge boson U. | result 0.99 | 0.73 | 0.40 | asserted 0.53 |
| s4 | The (collisional) damping of light candidates is, in some circumstances, large enough to be mentioned, but in most cases too small to generate a non linear matter power spectrum at the present epoch that differs significantly from the Cold Dark Matter spectrum. | result 0.95 | 0.72 | 0.07 | asserted 0.73 |
| s5 | On the other hand, heavier scalar dm particles (ie with $mdm \gtrsim O(GeV)$) turn out to be much less constrained. | result 0.99 | 0.83 | 0.11 | asserted 0.99 |
| s6 | We finally discuss a theoretical framework for scalar candidates, inspired from theories with N=2 extended supersymmetry and/or extra space dimensions, in which the dm stability results from a new discrete (or continuous) symmetry. | contribution 0.90 | 0.55 | 0.11 | asserted 0.84 |
What was examined, and what was not
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References
How later papers used it
303 later papers cite it
3 later papers by other authors are listed below: 1 used its method or tool and 2 compared their own results with it.
Uses its method or tool 1 paper
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Used the neutrino-DM coupling as described by the Feynman rule given in this paper.
Confusing the extragalactic neutrino flux limit with a neutrino propagation limit (2010) · 0.81 · paraphrased: the licence does not allow quoting
Compares with it 2 of 3 papers with this label
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Found that its s-wave component agrees with the one in Eq. (1) of this paper, while its p-wave component is different.
Scalar Dark Matter Candidates -- Revisited (2020) · 0.99 · paraphrased: the licence does not allow quoting
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Said that for C_hS = 0 and in the limit of M much greater than m_S much greater than m_f, its results agree with the calculation in this paper.
Dark top partner (2023) · 0.99 · paraphrased: the licence does not allow quoting
How the literature uses it
274 arXiv papers cite this in 327 sentences
Papers citing it · 178 sentences without a confident label
Contests it 1 paper
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Dark photons with mass $∼10 - 1$ were previously proposed as possible solutions [ref] , but these solutions are now excluded [ref] .
Resolving the $(g-2)_{\mu}$ and $B$ anomalies with leptoquarks and a dark Higgs boson · Introduction · contest 0.71
Uses its method or tool 1 paper
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In this work we use the $ν$-DM coupling as described by the Feynman rule [ref] shown in figure [ref] where $P_R$ denote the chiral projector, $ϕ$ stands for the spin-0 dark matter field and $g_νϕ$ denote the strength of its Yukawa coupling.
Confusing the extragalactic neutrino flux limit with a neutrino propagation limit · Introduction · 0.81
Compares with it 3 papers
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For the annihilation cross section via a $s$-channel $Z'$, the $s$-wave component vanishes as scalars have no spin, and the $p$-wave component reads [equation] It agrees with Eq. (3) in [ref] when taking $v_rel ≃2 v_ϕ$, where $v_ϕ$ is the DM velocity.
Scalar Dark Matter Candidates -- Revisited · DM annihilation · 0.93
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For both light and heavy mediators, the projected limits of a single thin-chip detector with 0.82 g$·$yr exposure surpass the existing constraints by orders of magnitude, including the limits from the direct detection of halo DM [ref] , and DM reflected from the sun [ref] , allowing to examine the benchmark freeze-in [ref] and freeze-out [ref] scenarios.
Novel Light Dark Matter Detection with Quantum Parity Detector Using Qubit Arrays · Introduction · 1.00
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Note that for $C_hS =0$ and in the limit of $M ≫m_S ≫m_f$, our results agrees with the calculation in Ref. [ref] .
Dark top partner · Relic density computation · 0.99
Cites it as support 1 paper
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Indeed, low-mass dark matter scenarios are typically only viable with additional low-mass mediators in the hidden sector [ref] .
Rare $Z$ Boson Decays to a Hidden Sector · Introduction · 0.97
Cites it as background 135 papers
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We will consider both complex scalar [ref] and pseudo-Dirac dark matter [ref] .
Impact of Resonance on Thermal Targets for Invisible Dark Photon Searches · Dark Photon Model · 0.91
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From a theoretical perspective, MeV-scale thermal dark matter candidates were shown to be viable some years ago [ref] and, since then, a large number of MeV-scale dark matter models have appeared in the literature, see e.g. [ref] .
Refined Bounds on MeV-scale Thermal Dark Sectors from BBN and the CMB · Introduction · 0.85
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The other scenario of interest which may impact the neutrino floor is constituted by a light scalar mediator that interacts with SM fermions [ref] .
How high is the neutrino floor? · Models · 0.84
Discussion
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